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When fast and slow interfaces grow together: Connection to the half-space problem of the Kardar-Parisi-Zhang class

Yasufumi Ito and Kazumasa A. Takeuchi*

  • Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

  • *kat@kaztake.org
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Phys. Rev. E 97, 040103(R) – Published 13 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.040103

Abstract

We study height fluctuations of interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class, growing at different speeds in the left half and the right half of space. Carrying out simulations of the discrete polynuclear growth model with two different growth rates, combined with the standard setting for the droplet, flat, and stationary geometries, we find that the fluctuation properties at and near the boundary are described by the KPZ half-space problem developed in the theoretical literature. In particular, in the droplet case, the distribution at the boundary is given by the largest-eigenvalue distribution of random matrices in the Gaussian symplectic ensemble, often called the GSE Tracy-Widom distribution. We also characterize crossover from the full-space statistics to the half-space one, which arises when the difference between the two growth speeds is small.

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Phys. Rev. E 97, 040103(R)– Published 13 April, 2018
  • Received 28 February 2018
Article part of CHORUS
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